Question

Tiana compares the length of a name on a nameplate to the number of letters in the name. She draws the scatterplot below, and then she plots and determines an equation for the trend line.

Nameplates
A graph has letters on the x-axis and length (inches) on the y-axis. A trend line goes through points (2, 5) and (4, 8). The regression equation is y = 1.47 x + 2.05.


Based on the information above, which is the best estimate of the number of letters that a name contains if the nameplate is 6 inches long?
3
4
10
12

Answer 1

To estimate the number of letters in a name if the nameplate is 6 inches long, we can use the regression equation provided:

\[ y = 1.47x + 2.05 \]

In this equation, \( y \) represents the length of the nameplate in inches, and \( x \) represents the number of letters in the name.

We want to find the value of \( x \) when \( y = 6 \):

\[ 6 = 1.47x + 2.05 \]

Now, we solve for \( x \):

1. Subtract 2.05 from both sides:

\[ 6 - 2.05 = 1.47x \]

\[ 3.95 = 1.47x \]

2. Now, divide both sides by 1.47:

\[ x = \frac{3.95}{1.47} \]

Calculating that gives:

\[ x \approx 2.68 \]

Since \( x \) must be a whole number (as it represents the number of letters), we round \( 2.68 \) to the nearest whole number, which is \( 3 \).

Thus, the best estimate of the number of letters that a name contains if the nameplate is 6 inches long is **3**.